Session V26: Quantum Resource Theories II

Resource-theory models for thermodynamics

The resource-theory framework is a mathematical toolkit developed in quantum information theory. The framework models transformations—of quantum states or probability distributions—under restricted classes of operations. Thermodynamics constrains operations to conserve energy. An agent may access easily only states thermal relative to the ambient temperature. Athermal states can carry more information than thermal states do, more accessible energy, and/or more coherence relative to the energy eigenbasis. These properties serve as resources in thermodynamic tasks. For example, work may be extracted from a bath hotter than the environment, via a heat engine. Thermodynamic resource theories (TRTs) are used to quantify athermal states’ value. Quantification measures include "one-shot" entropies beyond the Shannon, von Neumann, and relative entropies. TRTs extend to quantum systems that exchange conserved charges, analogous to heat and particles, that fail to commute. This talk will overview TRTs. The framework stretches statistical mechanics beyond equilibrium, to small (e.g., three-level) systems, to coherent quantum states, and to noncommuting charges.
  

The Quantum Cohering Power of Local Channels

The resource theory of quantum coherence studies coherence as a fundamental feature of quantum systems that can be converted from one form to another. Similar to the resource theory of entanglement, different measures of coherence have been proposed. The cohering power of a quantum channel can be defined, which is the maximum amount of coherence the channel can generate over all inputs. In this talk we show that the cohering power of certain channels can be increased when acting one half of an entangled state. In other words, the channel is able to generate more coherence on the joint system than on just the subsystem that it acts.

We then explore the connection between coherence and entanglement more closely. Specifically, we consider the problem of maximally increasing or decreasing the coherence of a bipartite state by local unitaries (LU). We show that when acting on two-qubit pure states, LU is just as powerful as nonlocal unitaries for increasing the coherence. In contrast, for decreasing the coherence (i.e. decoherence), LU is strictly weaker than nonlocal unitaries. We then compare the amount of decoherence that can be achieved by local unitaries to the amount of entanglement in the state.   

Subadditity of logarithmic violation of geometrical Bell inequalities for qudits.

Geometric inequalities for qubits [1] possess the highest robustness against the white noise among know correlation-based formulations. We present a construction of Bell inequalities for a collection of arbitrarily large subsystems (each with dimension d), with (d-1)-parameter family of local observables. The sum of outcomes of local measurments is represented as one of (d-1)-dimensional non-orthogonal vectors. We find the precise extimates of violation of the inequalities and observe that it grows exponentially with the number of (most probably) sublinearly with d. The intesting aspect is that we can compare the amount of nonclassiclity manifested in a single Bell experiment with subsystem that are composed of smaller parts with experiments conducted on these parts. The results of this comparison are counterintuitive.
[1] K. Nagata, W. Laskowski, M. Wiesniak, and M. Zukowski, Phys. Rev. Lett. 93, 23043 (2004)   

Local manipulation of multipartite entanglement

Many applications of quantum information rely on the potentiality of quantum systems to be correlated. For pure states, these correlations coincide with entanglement. Hence, the qualification and quantification of multipartite entanglement is one of the central topics within quantum information. However, as the dimension of the Hilbert space grows exponential with the number of considered subsystems, many very fundamental questions in this context are still unanswered.

In this talk I will focus on the local manipulation of multipartite entanglement contained in systems which are composed of n d-level subsystems [1,2,3]. Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. I will present the characterization of almost all LOCC transformations among pure states describing arbitrarily many subsystems which are of arbitrary local dimension (d). I will explain that non-trivial LOCC transformations among generic fully entangled pure states are almost never possible. Hence, almost all multipartite states are isolated. They can neither be deterministically obtained from local unitary (LU)-inequivalent states via local operations, nor can they be deterministically transformed to pure fully entangled LU-inequivalent states. I will then present a simple expression for the maximal probability to convert one multi-qudit fully entangled state to another for this generic set of states. The consequences of these findings in the context of entanglement theory will be discussed.

[1] G. Gour, B. Kraus, N. R. Wallach, J. Math. Phys. 58, 092204 (2017)
[2] D. Sauerwein, N. R. Wallach, G. Gour, B. Kraus, in preparation (2017).
[3] J. I. de Vicente, C. Spee, and B. Kraus, Phys. Rev. Lett. 111, 110502 (2013)   

Quantifying Genuine Multipartite Correlations and their Pattern Complexity

We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as: what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies which cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states which display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems. Reference: Phys. Rev. Lett. 119, 140505 (2017). LA-UR number LA-UR-17-29988   

The Entanglement Hierarchy of 2 x m x n Systems

We consider three partite pure states in the Hilbert space of dimensions 2,m,n and investigate to which states a given state can be locally transformed with a non-vanishing probability. Whenever the initial and final state are elements of the same Hilbert space, the problem is solved via the characterization of the SLOCC classes. However, when considering transformations from higher to lower dimensional Hilbert spaces, a hierarchy among the states can be found. We build on results presented in [1], where a connection to linear matrix pencils has been drawn in order to study SLOCC classes in 2,m,n systems. We first show that a generic set of states of dimensions 2,m,n, where n=m is the union of infinitely many SLOCC classes. However, for n≠m, there exists a single SLOCC class which is generic. Using this result, we derive a hierarchy of SLOCC classes for generic states. We also investigate common resource states, which are those states which can be transformed to any state (not excluding any zero-measure set) in the smaller dimensional Hilbert space.

[1] E. Chitambar, C.A. Miller, and Y. Shi, J. Math. Phys. 51, 072205 (2010)   

Optimising the distribution of entanglement in quantum networks

Quantum communication is one of the most promising technologies enabled by quantum mechanics, providing the potential to perform a host of useful tasks, including quantum key distribution and coin tossing. The holy grail of quantum communication is the creation of a quantum network, where a collection of end-users can exchange quantum information over long distances. In particular, a quantum network should be able to generate entanglement between any arbitrary pair of end-users, with the ability to make a trade-off between the generation time and the quality of the entanglement. That is, one would like to find a protocol that, for a fixed quality parameter, minimises the generation time. Here, we perform a restricted, numerical optimisation to find realistic protocols that can be implemented in a near-term quantum network. By exploring the parameter-space, we improve on known protocols and discover general heuristics for the distillation of entanglement over quantum networks.   

Dynamics of Entanglement and the Schmidt Gap in a Driven Light-Matter System

The ability to modify light-matter coupling in time (e.g. using external pulses) opens up the exciting possibility of generating and probing new aspects of quantum correlations in many-body light-matter systems. In the present work we study the impact of such a pulsed coupling on the light-matter entanglement in the Dicke model as well as the respective subsystem quantum dynamics. Our dynamical many-body analysis exploits the natural partition between the radiation and matter degrees of freedom, allowing us to explore time-dependent intra-subsystem quantum correlations by means of squeezing parameters, and the inter-subsystem Schmidt gap for different pulse duration (i.e. ramping velocity) regimes - from the near adiabatic to the sudden quench limits. Our results reveal that both types of quantities indicate the emergence of the superradiant phase when crossing the quantum critical point. In addition, at the end of the pulse light and matter remain entangled even though they become uncoupled, which could be exploited for engineering protocols to generate entangled states in non-interacting systems.   

Entanglement spectrum of engineered NMR spin Hamiltonians

Experimentally characterizing the complexity of many-body quantum dynamics in physical systems is a challenging task. A new correlation metric, similar to an out-of-time-ordered correlator (OTOC), was recently used to experimentally characterize the transition between a non-interacting, Anderson localized phase, and an interacting many-body localized phase in a model NMR system [1]. Here we use eigenvalue spectrum statistics (ESS) to study the properties of this class of experimentally accessible spin Hamiltonians that can be implemented in solid-state NMR experiments. ESS has recently gained attention for the ability to differentiate between different dynamical phases in simulations. We show that this model does indeed display a rich dynamical behavior, showing Poisson, Gaussian Orthogonal Ensemble (GOE), and Gaussian Unitary Ensemble (GUE) distributions in different experimentally-accessible parameter regimes. These results can guide the design of NMR OTOC experiments to probe these dynamical transitions.

[1] K. X. Wei, C. Ramanathan, P. Cappellaro, Exploring Localization in Nuclear Spin Chains, (2016)